Is it possible??? Depends...in how many days...how soon, and do you have Chick-On like hiking abilities...yes or no?
Seriously, The two most direct (assuming you want to stay on trail) ways to get from Tuolumne to Merced Lake are via Vogelsang or Cathedral Lakes to Sunrise Camp and then to Merced Lake. Since the Hiogh Sierra Camps (Merced Lake, Vogelsang, and Sunrise) are each about a day's reasonable hike away from each other, you are talking about 2 "normal" hiking days (in anything but normal scenery) to get from Tuolumne to Merced. Both ways are about 16+/- miles total.
Sure, you can also start at Tenaya, go up Clouds Rest via the Sunrise Trail, and then probably go down Sunrise Creek, camp there, and then head to Merced the next day. This is probably a mile or two farther...assuming you want to get to the top of Clouds Rest...if not its a couple of miles shorter. If you are going this way soon, check out the info
here re water crossing and snow (melting quickly now)